The only Pretty Cure I am knowledgeable of enough to discuss (and have seen in its entirety) is Yes! PreCure 5 / PreCure 5 Go Go (and that is exclusively because I watch everything and I mean everything ever that has Irino Miyu in it). For those unfamiliar, Irino Miyu (aka Sora) voices a talking chipmunk/squirrel thing and it is glorious.
I am not familiar with the dub name you are talking about though? Maybe from a different season.
ANYWAY...
One of the fun things about PreCure, for me at least, was that it was mostly the girls able to solve their own problems by using the power of their hearts, empathy and courage to fix problems, not on sheer battle ability. I could see this working in KH pretty easily. As far as actual story/gameplay mechanics...
In the PreCure 5 universe, the world was being overrun by "nightmares" that needs to be defeated by the power of heart and various dreams (Pinkies) that the girls spent most of the season collecting. Perhaps that could be made into some sort of fetching mini game, where Sora has to assist them in finding Pinkies that were scattered around to other worlds that they can't locate. Then...maybe upon finding them all you could return and have to face off against a big nightmare with the girls. And, since we are trying to mesh them together, perhaps the nightmares are some type of subset of unversed?
It would be fun if, perhaps, this could somehow be tied into a way to redeem Vanitas' character if, somehow, he is still around after KH3 and is still being all evil. Part of the finale of the series was about seeing the heart in your enemy and breaking through to it, so it would potentially be possible to have this be a setting to finally break through and make Vanitas not such a creepo.
*shrugs*
I don't really know too much about the other series' plotlines to actually come up with something that would work with those. Honestly, I feel like having Sora join a magical girl team would be way too precious and I would love it, ESPECIALLY if he gets his own transformation sequence.
OR, you know what?
Have Kairi do it. I'd be down for that.